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The lecture begins with a question-and-answer session about black holes. Topics include the extent to which we are sure black holes exist in the center of all galaxies, how massive they are, and how we can observe them. The lecture then turns to strong-field relativity: relativistic effects that are unrelated to Newtonian theory. The possibility of testing predictions of the existence of black holes is discussed in the context of strong-field relativity. One way we might learn about black holes is through observation of the orbit of the companion star in an X-ray binary star system. Through this we can estimate the mass of the compact object. The lecture ends with an explanation of how astronomers find black holes, and how Professor Bailyn was able to discover one himself.

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Professor Bailyn begins with a summary of the four post-Newtonian effects of general relativity that were introduced and explained last time: precession of the perihelion, the deflection of light, the gravitational redshift, and gravitational waves. The concept of gravitational lensing is discussed as predicted by Einstein’s general relativity theory. The formation of a gravitational lens can be observed when light from a bright distant source bends around a massive object between the source (such as a quasar) and the observer. Professor Bailyn then offers a slideshow of gravitational lenses. The issue of finding suitable astronomical objects that lend the opportunity to observe post-Newtonian relativistic effects is addressed. The lecture ends with Jocelyn Bell and the discovery of pulsars.

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Class begins with clarification of equations from the previous lecture. Four post-Newtonian gravitational effects are introduced and discussed in detail. The first of these is the so-called Perihelion Precession, which occurs when the major axis of a planet’s elliptical orbit precesses within its orbital plane, in response to changing gravitational forces exerted by other planets. Secondly, deflection of light is described as the curving of light as it passes near a large mass. Gravitational redshift is explained as a frequency effect that occurs as light moves away from a massive body such as a star or black hole. Finally, the existence and effects of gravitational waves are discussed. The lecture closes with a brief history of the 1919 eclipse expedition that made Einstein famous.

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One last key concept in Special Relativity is introduced before discussion turns again to black celestial bodies (black holes in particular) that manifest the relativistic effects students have learned about in the previous lectures. The new concept deals with describing events in a coordinate system of space and time. A mathematical explanation is given for how space and time reverse inside the Schwarzschild radius through sign changes in the metric. Evidence for General Relativity is offered from astronomical objects. The predicted presence and subsequent discovery of Neptune as proof of General Relativity are discussed, and stellar mass black holes are introduced.

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The lecture begins with a comprehensive overview of the historical conditions under which Einstein developed his theories. Of particular impact were the urgent need at the turn of the 19th century to synchronize clocks around the world; Einstein’s position at a patent office; and a series of experiments that he himself carried out. In 1905 Einstein published three papers that are still considered the greatest papers in the field of physics. The lecture then moves to General Relativity and how it encompasses Newton’s laws of gravity. A visual demonstration shows how space-time undergoes curvature when mass is introduced. Class ends with a question-and-answer period on a variety of topics in Special Relativity.

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The lecture begins with the development of post-Newtonian approximations from Newtonian terms. Several problems are worked out in calculating mass, force and energy. A discussion follows about how concepts like mass and velocity are approached differently in Newtonian physics and Relativity. Attention then turns to the discovery that space and time change near the speed of light, and how this realization affected Einstein’s theories. Finally, the possibility of traveling faster than the speed of light is addressed, including how physicists might predict from laboratory conditions how this might occur. Muons, unstable particles that form at the top of the Earth’s atmosphere, are used as an example.

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The discussion of black holes continues with an introduction of the concept of event horizon. A number of problems are worked out to familiarize students with mathematics related to black hole event horizons. In a longer question and answer session, Professor Bailyn discusses the more mystifying aspects of the nature of black holes and the possibility of time travel. Finally, the issues of reconciling Newton’s laws of motion with Special Relativity, and Newton’s law of gravity with General Relativity, are addressed.

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The second half of the course begins, focusing on black holes and relativity. In introducing black holes, Professor Bailyn offers a definition, talks about how their existence is detected, and explains why (unlike in the case with exoplanets where Newtonian physics was applied) Einstein’s Theory of Relativity is now required when studying black holes. The concepts of escape and circular velocity are introduced. A number of problems are worked out and students learn how to calculate an object’s escape velocity. A historical overview is offered of our understanding and discovery of black holes in the context of stellar evolution.

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Class begins with a problem on transits and learning what information astronomers obtain through observing them. For example, radii of stars can be estimated. Furthermore, applying the Doppler shift method, one can find the mass of a star. Finally, a star’s density can be calculated. A second method for identifying planets around stars is introduced: the astrometry method. The method allows for an extremely accurate assessment of a star’s precise position in the sky. Special features of the astrometry method are discussed and a number of problems are solved. A short summary is given on the three methods astronomers use to identify exoplanets. Class ends with an overview of upcoming space missions and the hope of detecting the presence of biological activity on other planet.

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The class begins with a discussion on transits – important astronomical events that help astronomers to find new planets. The event occurs when a celestial body moves across the face of the star it revolves around and blocks some of its light. By calculating the amount of light that is being obscured astronomers can obtain important information about both star and planet, such as size, density, radial velocity and more. The concept of planetary migration is explained in order to better understand the dramatic differences between bodies in the Inner and Outer Solar System. Finally, potential problems in the Solar System that may occur as a result of migration are addressed.